Question 1121174
A and B working together can complete a job in 30 days.
 After they had both worked 18 days, however, A left and B finished the work in 20 more days.
 Find the time in which each can do the work alone.
:
let a = time A required to complete the job alone
let b = time for B alone
let the completed job = 1
:
Write an equation for each statement
"A and B working together can complete a job in 30 days."
{{{30/a}}} + {{{30/b}}} = 1
multiply eq by ab
30b + 30a = ab
"After they had both worked 18 days, however, A left and B finished the work in 20 more days."
{{{18/a}}} + {{{38/b}}} = 1
18b + 38a = ab
:
ab = ab therfore
18b + 38a = 30b + 30a
38a - 30a = 30b - 18b
8a = 12b
a = {{{12/8}}}b
a = 1.5b
:
Using the first equation, replace a with 1.5b
{{{30/(1.5b)}}} + {{{30/b}}} = 1
multiply by b
{{{30/1.5}}} + 30 = b
20 + 30 = b
b = 50 hrs B working alone
then find a
1.5(50) = 75 hrs b working alone